Question

(5-1) If you deposit $2,600 dollars in an account today that pays 5.70% compound interest (compounded annually), how much will accumulate in the account at the end of eight years? (5-2) In the question above, how much will accumulate if the account pays simple interest rather than compound interest? (5-3) If you wish to accumulate $25,000 in twenty years, how much must you deposit today in an account paying 4.25%? (5-4) If you can deposit $15,000 in an account today, and withdraw $40,000 in 25 years, what effective rate is the account paying?

SHOW STEP BY STEP HOW TO SOLVE

ANSWERS:

5-1 $4,051.10

5-2 $3,785.60

5-3 $10,874.74

5-4 4.00%

Answer 1

This question requires application of basic time value of money function, according to which EV PV (1 where FV is Future Value, PV is present value, n is number of periods and r is rate per period

Question 5-1

FV = $2600 * (1 + 5.70%)⁸

FV = $2600 * 1.5581

FV = $4,051.10

Question 5-2

Simple Interest = Principle * Rate * Time

Simple Interest = $2600 * 5.7% * 8 = $1,185.60

Total Amount accumulated = $2,600 + $1,185.60 = $3,785.60

Question 5-3

$25,000 = PV * (1 + 4.25%)²⁰

$25000 = PV * 2.2989

PV = $10,874.74

Question 5-4

$40000 = $15000 * (1 + r)²⁵

2.6667 = (1 + r)²⁵

1.0400 = 1+ r

r = 4.00%